To wring something is to twist or squeeze it, usually out of its original shape. If you annoy someone enough, they might threaten to wring your neck.
If you do laundry by hand, then you most likely wring out your shirts to get rid of excess water before hanging them out to dry. You can also wring out someone's hair after washing it. As you can tell, the word often has to do with getting liquids out of something. You might wring tears out of a person's eyes if you tell him the sad story of the day you lost your puppy.